Maclaurin and Power Series Q1

By considering the series expansions of \({\ln \left( 1-{{x}^{2}} \right)}\) and \({\ln \left( \frac{1+x}{1-x} \right)}\), or otherwise, find the exact value of the following series.

\({\sum\limits_{r=1}^{\infty }{\left[ \left( \frac{1}{2r}+\frac{1}{2r+1} \right){{\left( \frac{1}{4} \right)}^{r}} \right]}}\).